Question

Two conducting spheres of radius 5cm and 10cm are given a charge of 15micro coulmb each. After the two spheres are jointed by a conducting wire , the charge on the smaller sphere (is there a shortcut way to solve this question)

Answer 1

I think Charge on the smaller sphere is 10 microcoulomb.

Explanation:

As we know that after connecting the wire the potential of both the sphere will be equal.
Let q1 and q2 be the charge on small and large spheres respectively
Also, q1 + q2 = 30 micro columb (before and after connecting the wire.

Now the shortcut
V1 = V2
Kq1/r1 = Kq2/r2
q1/5 = q2/ 10
2q1 = (30 - q1)

q1 = 10 micro columb